Beveling with tight geometry
Beveling such thing is not an easy, because of small cuts (like objects under Boolean.003, .007, .008). Beveled edges starts to overlap. So you can use only some small range, but even with the value 0.003 it is overlapping. You can notice that since bevelling doesn't appear until you disable Clamp Overlap under Geometry or disable mentioned modifiers.

If you need bevel bigger radius in some areas than others (like bigger radius on base shape and smaller on smaller cuts) move Bevel Modifier up in modifier's stack and use another one.
You would have to use probably some limitations, like Vertex Group for those vertices. But Vertex Group can be set only when modifiers are applied, means destructive way.

Some decent bevelling can be achieved with material Bevel node.